David Cameron speaks during prime minister's questions in the House of Commons today. Photograph: PA

David Cameron has confirmed that the government will comply with a supreme court human rights ruling giving thousands of sex offenders the chance of not being "labelled for life" despite Theresa May saying the government was appalled by the decision.

The prime minster told MPs he would do only "the minimum necessary" to comply with the landmark ruling, made last April, and tried to assuage backbench Tory anger at the impact of another human rights ruling by announcing that a commission to look at a creating British bill of rights would be set up "imminently".

"It is time to assert that parliament makes our laws, not the courts, that the rights of the public come before the rights of criminals and, above all, that we have a legal framework that brings sanity to cases such as these," the home secretary, Theresa May said in a statement to MPs.

The decision to set up the commission was previously pencilled in for later this year with no end date fixed for it to report.

But the row over the sex offenders ruling under the European convention on human rights – which comes hard on the heels of the controversy over votes for prisoners – appears to have speeded up the process.

The supreme court ruling said the 24,000 people on the sex offender register in England and Wales had a right to a review of whether they should continue to be "labelled for life" by being kept on the register indefinitely.

The judges based their decision on Home Office evidence that 75% of sex offenders who were monitored for 21 years were not reconvicted of any further offence.

The home secretary told MPs that although the government had been appalled by the ruling there was no possibility of further appeal, and the "minimum possible changes to the law" would be made to comply with the ruling.

No sex offender will be allowed to apply for a review of their inclusion on the register until 15 years after they have been released from custody. The police, not the courts, are to be given the final say on whether they are taken off the register.

"There will be no automatic appeals," May said. "We will deliberately set the bar for those appeals as high as possible.

"Public protection must come first. A robust review led by the police, and involving all relevant agencies, will be carried out so that a full picture of the risks to the public can be considered."

It would have been expected that the parole board or another judicial panel might have had the final say on whether an individual sex offender posed a continuing risk to the public more than 15 years year after they had been released from prison.

But May said the police were best placed to assess the continuing risk.

She also confirmed that several loopholes previously identified in the register were now to be closed.

They include making it compulsory to report to the police when travelling abroad for a single day rather than the current minimum of three days, to tell the police when an offender is living in a household with a child under 18, and ensuring they remain on the register if they change their name by deed poll.

Harry Fletcher, of the probation union, Napo, said the register was one of a number of tools that the police and probation services had to control the behaviour of relevant offenders.

"There will have to be a very rigorous assessment conducted before an appeal to remove a name from the register is heard," he said.

"It is highly likely that very few appeals will be successful. Persons placed on the register for life have been convicted of very serious offences. This decision will not diminish public protection."

The supreme court ruling last year came after a case brought by two offenders, a teenager convicted of rape and a 59-year-old man guilty of indecent assault.

The teenage boy, known only as F, had been jailed for 30 months in October 2005, aged 11, for raping a six-year-old boy.

The second case involved a man named Angus Aubrey Thompson, who was jailed for five years in 1996.

Both offenders said their lifelong registration with no chance of a review was a disproportionate interference in their family lives.

Mark Williams-Thomas, a former police officer who worked in child protection, disputed the idea that sex offenders could be rehabilitated or treated, saying: "These people are like leopards – they don't change their spots.

"These people are very devious. What we will end up with is potentially a very dangerous situation where someone has committed offences in the past and be able to say they haven't committed any new offences and therefore don't present a risk.

"But they are a risk in the same way as an alcoholic is always an alcoholic."